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Popular >

derivative of \sqrt[3]{9x^2+8}

Solution

derivative of

3 9 x^{2} + 8

Solution

\frac{6 x}{( 9 x ^{2} + 8 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (3 9 x^{2} + 8)

Apply the chain rule:

\frac{1}{3 ( 9 x ^{2} + 8 ) ^{\frac{2}{3}}} \frac{d}{d x} (9 x^{2} + 8)

= \frac{1}{3 ( 9 x ^{2} + 8 ) ^{\frac{2}{3}}} \frac{d}{d x} (9 x^{2} + 8)

\frac{d}{d x} (9 x^{2} + 8) = 18 x

= \frac{1}{3 ( 9 x ^{2} + 8 ) ^{\frac{2}{3}}} \cdot 18 x

Simplify

\frac{1}{3 ( 9 x ^{2} + 8 ) ^{\frac{2}{3}}} \cdot 18 x : \frac{6 x}{( 9 x ^{2} + 8 ) ^{\frac{2}{3}}}

= \frac{6 x}{( 9 x ^{2} + 8 ) ^{\frac{2}{3}}}

Graph

Popular Examples

derivative of (4x^5-8x/(x^3))

\frac{d}{d x} (\frac{4 x ^{5} - 8 x}{x ^{3}})

(\partial)/(\partial x)(7e^{6x}sin(5y))

\frac{\partial}{\partial x} (7 e^{6 x} sin (5 y))

integral of 1/(sqrt(n^2-1))

\int \frac{1}{n ^{2} - 1}

tangent of y=3x^3-3x,(1,0)tangent of

y = 3 x^{3} - 3 x, (1, 0)

(dy)/(dx)=2y^2(x+1)

\frac{d y}{d x} = 2 y^{2} (x + 1)

Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{9x^2+8} ?
The derivative of \sqrt[3]{9x^2+8} is (6x)/((9x^2+8)^{2/3)}
What is the first derivative of \sqrt[3]{9x^2+8} ?
The first derivative of \sqrt[3]{9x^2+8} is (6x)/((9x^2+8)^{2/3)}